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Answer:
Step-by-step explanation:
The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)
Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through is:
.
Therefore the line passing through (2, 4) and (4, -2) has an equation:
Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10
Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:
.
Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:
Since it is the perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:
the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is